The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis: the adsorption sites are uniformly distributed on the surface of the pore walls in the adsorbent, the sorption sites are uniformly distributed in the volume of the polymer. In this first paper we will analyze the simple case where one solute molecule is only allowed to occupy a single adsorption or sorption site. A common elementary occupation law of the free sites is assumed: the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free (non-occupied) sites in the solid. The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute. In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by themolarity. The simple monolayer adsorption law of Jovanovic is obtained: n = n(0) (1 - e(-KP)) where n is the number of moles adsorbed when the pressure is P. n(0) is the total number of adsorption sites and K the affinity coefficient for adsorption. The sorption law writes: a = 1/k inverted right perpendicular phi/1-phi inverted left perpendicular + 1-r/k ln inverted right perpendicular 1 + 1/r phi/phi-1 inverted right perpendicular where phi , r and k hold respectively for the volume fraction of the solvent in the polymer, for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient. The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations: the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results. (C) 2017 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.